If you are talking about being inside a passenger elevator, you would say “I am in the elevator”. But elevators in factories and in garages (for vehicles) aren’t enclosed. So you would use “on” in those cases. Also, in AmE at least, you can “get on an elevator”. “Excuse me, Sir. How do I get to the restaurant?” “Get on the elevator and take it to the 8th floor.”

“In the elevator” is correct.

We would say "I'm in the elevator"

In the elevator is correct.